Question

Which point lies inside the circle with equation (x - 2)2 + (y + 3)2 = 4?

(2, -4)

(2, 0)

(0, -3)

(2, -5)

Answer 1

(0, -3) is the answer. Plug all the options into the equation and the only one that works is (O, -3)

Answer 2

(C) and (D)

Explanation:

The given equation of the circle is:

`(x-2)^2+(y+3)^2=4`

A. Substitute the value of x=2 and y=-4 in the given equation, we have

`(2-2)^2+(-4+3)^2=4`

`1=4`

which is not possible, thus (2,-4) does not lie in the given equation.

B. Substitute the value of x=2 and y=0 in the given equation, we have

`(2-2)^2+(0+3)^2=4`

`9=4`

which is not possible, thus (2,0) does not lie in the given equation.

C.Substitute the value of x=0 and y=-3 in the given equation, we have

`(0-2)^2+(-3+3)^2=4`

`4=4`

which is possible, thus (0.-3) lies in the given equation.

D.Substitute the value of x=2 and y=-5 in the given equation, we have

`(2-2)^2+(-5+3)^2=4`

`4=4`

which is possible, thus (2,-5) lies in the given equation.